Texas Sen. Ted Cruz and Jay Leno sparred on issues ranging from gun control to gay marriage during the Tea Party favorite's first appearance on The Tonight Show.

Cruz, a Republican elected in 2012 to fill the seat vacated by the retiring Kay Bailey Hutchison, came to the Tonight Show after gaining national attention for filibustering against Obamacare and sparking the government shutdown. He also recently held up the confirmation of FCC chairman Thomas Wheeler.

Leno pressed Cruz on the possibility of another government shutdown, asking, "Are we going to have another shutdown in February?"

"Look, I certainly hope not," Cruz said, to which Leno rejoined "Have you stockpiled some books to read for this one?" (Cruz famously read from Dr. Seuss during his filibuster.)

Leno challenged Cruz on his opposition to Obamacare, noting 25 percent of Texans were uninsured, so "Obamacare would help them, wouldn't it?"

Not so, said Cruz, who called Obamacare the "biggest job killer in this country."

"We ought to empower patients, rather than government bureaucrats getting between you and your doctor," Cruz said to applause.

Leno also questioned why some Republicans focused on social issues, asking Cruz to explain his stance against gay marriage.

"I support marriage between one man and one woman, but I also think it's a question for the states," Cruz said. "Some states have made decisions one way on gay marriage; some states have made decisions the other way. And that's the great thing about our Constitution, is different states can make decisions depending on the values."

Leno also pressed Cruz on his opposition to tougher background checks for gun buyers.

"Why is increased or better background checks not a good thing? You voted against this," Leno said.

Cruz touted an alternative gun control bill he co-sponsored, which would give more resources to prosecutors for gun law violations and create a task force to prosecute people who fail criminal background checks.

"Do you target violent criminals, or do you try to take away the constitutional rights of law-abiding citizens?" Cruz asked.

Cruz was the latest in a string of political guests on Tonight in recent months. In August, Leno welcomed President Obama, while last month Ann Romney, wife of former GOP presidential candidate Mitt Romney, appeared to discuss her cook book.